Question

What is the value of $1,{111}^2$?

• A. $121$
• B. $12,321$
• C. $1,234,321$
• D. $123,454,321$

Answer 1

The correct option is C $1,234,321$

To find the square of numbers that consist of repeated $1$'s such as ${11}^2$, ${111}^2$, $1,{111}^2$, etc.:

$\bullet$ Count the number of $1$'s in the given number;
$\bullet$ Write starting from $1$ till the number of $1$'s;
$\bullet$ Concatenate the reverse counting upto $1$ with the last digit

For an example, let's say we need to find ${111}^2$:
$\bullet$ $111$ consists of three $1$'s;
$\bullet$ Write starting from $1$ till the number of $1$'s; hence, $\underset{–}{123}$;
$\bullet$ Concatenate the reverse counting upto $1$ with the last digit; hence, $123\underset{–}{21}$
$\therefore \underset{–}{{111}^2=12,321}$

Finally, we need to find the value of $1,{111}^2$.
$\bullet$ $1,111$ consists of four $1$'s;
$\bullet$ Write starting from $1$ till the number of $1$'s; hence, $\underset{–}{1234}$;
$\bullet$ Concatenate the reverse counting upto $1$ with the last digit; hence, $1234\underset{–}{321}$
$\therefore \underset{–}{1,{111}^2=1,234,321}$

Therefore, option (c.) is the correct answer.